Is a baby's birth covered by his father's insurance even though his parents are not married?

Birth might not be, as this really relates to the woman's health care, but post-birth care could be if the father includes the child on his plan. I would contact the health provider to explain the situation and explore options. If you are not able to obtain insurance for the mother through his plan, I strongly suggest that she obtain prenatal care through a free or sliding-scale clinic. Don't let the insurance situation deter you from getting her and the baby proper care.